Question 4:

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).

Answer:

p(x) = x³ − 3x² + x + 2 (Dividend)

g(x) = ? (Divisor)
Quotient = (x − 2)
Remainder = (− 2x + 4)
Dividend = Divisor × Quotient + Remainder

x³ – 3x² +x + 2 = g(x) × (x – 2) + (−2x + 4)

x³ – 3x² + x + 2 + 2x – 4 = g(x) (x – 2)

x³ – 3x² +3x – 2 = g(x) (x – 2)

g(x) is the quotient when we divide (x³ – 3x² +3x – 2) by (x – 2)

∴ g(x) = (x² – x + 1)

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